Solve [-1+3/2-(-3/4-(-1-1/6))]sqrt{2-frac{7/4}}{(-frac{5}{3})^-1+frac{1}{2}-(-2)^-2}

$$\frac { [ - 1 + \frac { 3 } { 2 } - ( - \frac { 3 } { 4 } - ( - 1 - \frac { 1 } { 6 } ) ) ] \sqrt { 2 - \frac { 7 } { 4 } } } { ( - \frac { 5 } { 3 } ) ^ { - 1 } + \frac { 1 } { 2 } - ( - 2 ) ^ { - 2 } }$$

Evaluate

$$-\frac{5}{42}\approx -0.119047619$$

Solution Steps

Add -1 and \frac{3}{2} to get \frac{1}{2}.

$$\frac{\left(\frac{1}{2}-\left(-\frac{3}{4}-\left(-1-\frac{1}{6}\right)\right)\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Subtract \frac{1}{6} from -1 to get -\frac{7}{6}.

$$\frac{\left(\frac{1}{2}-\left(-\frac{3}{4}-\left(-\frac{7}{6}\right)\right)\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

The opposite of -\frac{7}{6} is \frac{7}{6}.

$$\frac{\left(\frac{1}{2}-\left(-\frac{3}{4}+\frac{7}{6}\right)\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Add -\frac{3}{4} and \frac{7}{6} to get \frac{5}{12}.

$$\frac{\left(\frac{1}{2}-\frac{5}{12}\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Subtract \frac{5}{12} from \frac{1}{2} to get \frac{1}{12}.

$$\frac{\frac{1}{12}\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Subtract \frac{7}{4} from 2 to get \frac{1}{4}.

$$\frac{\frac{1}{12}\sqrt{\frac{1}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{12}\times \frac{1}{2}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Multiply \frac{1}{12} and \frac{1}{2} to get \frac{1}{24}.

$$\frac{\frac{1}{24}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Calculate -\frac{5}{3} to the power of -1 and get -\frac{3}{5}.

$$\frac{\frac{1}{24}}{-\frac{3}{5}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Add -\frac{3}{5} and \frac{1}{2} to get -\frac{1}{10}.

$$\frac{\frac{1}{24}}{-\frac{1}{10}-\left(-2\right)^{-2}}$$

Calculate -2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{24}}{-\frac{1}{10}-\frac{1}{4}}$$

Subtract \frac{1}{4} from -\frac{1}{10} to get -\frac{7}{20}.

$$\frac{\frac{1}{24}}{-\frac{7}{20}}$$

Divide \frac{1}{24} by -\frac{7}{20} by multiplying \frac{1}{24} by the reciprocal of -\frac{7}{20}.

$$\frac{1}{24}\left(-\frac{20}{7}\right)$$

Multiply \frac{1}{24} and -\frac{20}{7} to get -\frac{5}{42}.

$$-\frac{5}{42}$$

Factor

$$-\frac{5}{42} = -0.11904761904761904$$